def test_integrated_process(ar_params, diff, ma_params, sigma2):
# Test loglikelihood computation when model has integration
nobs = 100
endog = np.cumsum(np.random.normal(size=nobs))
# Innovations algorithm approach
llf_obs = arma_innovations.arma_loglikeobs(
np.diff(endog, diff), ar_params, ma_params, sigma2)
# Kalman filter apparoach
mod = SARIMAX(endog, order=(len(ar_params), diff, len(ma_params)),
simple_differencing=True)
res = mod.filter(np.r_[ar_params, ma_params, sigma2])
# Test that the two approaches are identical
assert_allclose(llf_obs, res.llf_obs)
def test_integrated_process(ar_params, diff, ma_params, sigma2):
# Test loglikelihood computation when model has integration
nobs = 100
endog = np.cumsum(np.random.normal(size=nobs))
# Innovations algorithm approach
llf_obs = arma_innovations.arma_loglikeobs(
np.diff(endog, diff), ar_params, ma_params, sigma2)
# Kalman filter apparoach
mod = SARIMAX(endog, order=(len(ar_params), diff, len(ma_params)),
simple_differencing=True)
res = mod.filter(np.r_[ar_params, ma_params, sigma2])
# Test that the two approaches are identical
assert_allclose(llf_obs, res.llf_obs)
def test_innovations_algo_filter_kalman_filter(ar_params, ma_params, sigma2):
# Test the innovations algorithm and filter against the Kalman filter
# for exact likelihood evaluation of an ARMA process
endog = np.random.normal(size=100)
# Innovations algorithm approach
llf = arma_innovations.arma_loglike(endog, ar_params, ma_params, sigma2)
llf_obs = arma_innovations.arma_loglikeobs(endog, ar_params, ma_params,
sigma2)
score = arma_innovations.arma_score(endog, ar_params, ma_params, sigma2)
score_obs = arma_innovations.arma_scoreobs(endog, ar_params, ma_params,
sigma2)
# Kalman filter apparoach
mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params)))
params = np.r_[ar_params, ma_params, sigma2]
# Test that the two approaches are the same
assert_allclose(llf, mod.loglike(params))
assert_allclose(llf_obs, mod.loglikeobs(params))
# Note: the tolerance on the two gets worse as more nobs are added
assert_allclose(score, mod.score(params), atol=1e-5)
assert_allclose(score_obs, mod.score_obs(params), atol=1e-5)
def test_regression_with_arma_errors(ar_params, ma_params, sigma2):
# Test loglikelihood computation when model has regressors
nobs = 100
eps = np.random.normal(nobs)
exog = np.c_[np.ones(nobs), np.random.uniform(size=nobs)]
beta = [5, -0.2]
endog = np.dot(exog, beta) + eps
# Innovations algorithm approach
beta_hat = np.squeeze(np.linalg.pinv(exog).dot(endog))
demeaned = endog - np.dot(exog, beta_hat)
llf_obs = arma_innovations.arma_loglikeobs(
demeaned, ar_params, ma_params, sigma2)
# Kalman filter approach
# (this works since we impose here that the regression coefficients are
# beta_hat - in practice, the MLE estimates will not necessarily match
# the OLS estimates beta_hat)
mod = SARIMAX(endog, exog=exog, order=(len(ar_params), 0, len(ma_params)))
res = mod.filter(np.r_[beta_hat, ar_params, ma_params, sigma2])
# Test that the two approaches are identical
assert_allclose(llf_obs, res.llf_obs)
def test_regression_with_arma_errors(ar_params, ma_params, sigma2):
# Test loglikelihood computation when model has regressors
nobs = 100
eps = np.random.normal(nobs)
exog = np.c_[np.ones(nobs), np.random.uniform(size=nobs)]
beta = [5, -0.2]
endog = np.dot(exog, beta) + eps
# Innovations algorithm approach
beta_hat = np.squeeze(np.linalg.pinv(exog).dot(endog))
demeaned = endog - np.dot(exog, beta_hat)
llf_obs = arma_innovations.arma_loglikeobs(
demeaned, ar_params, ma_params, sigma2)
# Kalman filter approach
# (this works since we impose here that the regression coefficients are
# beta_hat - in practice, the MLE estimates will not necessarily match
# the OLS estimates beta_hat)
mod = SARIMAX(endog, exog=exog, order=(len(ar_params), 0, len(ma_params)))
res = mod.filter(np.r_[beta_hat, ar_params, ma_params, sigma2])
# Test that the two approaches are identical
assert_allclose(llf_obs, res.llf_obs)